Abstract

We consider the initial value problem on the circle for a cubic nonlinear schrodinger equation governed by a higher-ordereven dispersion operator Dα with an even integer exponent α>2. Our main result proves that the uniform radius of spatialanalyticity σ (t) survives over time, satisfying a lower bound decay rate of c|t|-1 for a positive constant c. To overcome thederivative losses and track the evolution of the analytic radius, we construct a higher-order almost conservation law inGevrey spaces. The analytical framework incorporates Duhamel’s formula, Strichartz estimates for the linear wave,trilinear estimates, Plancherel’s identity, Holder’s inequality, and Sobolev embeddings.